Without a cube, luck would play more into a game - but like furbster said - would probable be just as fun without the cube.
One of the reasons I suggest Hypergammon is that is uses the same rules as regular backgammon, so little new programming would be needed.
Some other Gammon variant suggestions I have, but of course each would take more programming and such so would be more time to make are:
1) A mix between Tabula gammon and Russian Gammon. Basicly like "race", all pieces start off the board - BOTH players race the same direction around the board, bring in their pieces in the same area - can only move their pieces 1/2 way around the board until all of their pieces have entered the board - 2 dice only - no special double rules - rest of the rules like current gammon/race rules.
2) Domino-Gammon - I have since seen some other versions talked about, but linked are the rules that I have made up for the game.